Simplifying Rational Expressions: Key Concepts and Techniques

This video tutorial covers simplifying rational expressions using various examples. It begins with an introduction to accessing a free worksheet and proceeds to demonstrate simplification techniques using laws of exponents and factoring. Each example focuses on different variables and coefficients, illustrating how to simplify expressions step-by-step. The video concludes with a reminder to simplify both numerators and denominators for complete expression simplification.

What is the first step in simplifying the expression 36x^3 over 42x^2?

• Divide by the greatest common divisor of 36 and 42.

• Add the exponents in the expression.

• Multiply the numerator and denominator by the lowest common multiple.

• Subtract the coefficients of the variables.

When simplifying the expression with bases x^3 over x^2, what is the resulting exponent of x?

• x^1

• x^5

• x^6

• x^0

In the expression R^2 over R^3, what is the simplified form?

• 1 over R

• R

• R^5

• R^1

How do you simplify a fraction where both the numerator and the denominator are divisible by 4?

• None of the above

• Multiply both by 4

• Divide both by 4

• Add 4 to both numerator and denominator

What happens to the variable n in the expression n^2 over n?

• It is squared

• It is cubed

• It cancels out leaving n

• It remains unchanged

What is the result of simplifying the expression 70n^2 over 28n?

• 2 over 5n

• 2n over 5

• 5 over 2n

• 5n over 2

In the expression 15n over 30n^3, what is the simplified form?

• 2 over n^2

• 2n^2 over 1

• 1 over 2n^2

• 1 over 2n

What simplification occurs when you factor out a common term from a binomial in the numerator?

• The terms cancel out

• The expression becomes a monomial

• The denominator is eliminated

• None of the above

After pulling out a common factor of 10 from the denominator, what is the simplified form of 45 over 10(a - 1)?

• 9 over 2(a - 1)

• 4.5 over (a - 1)

• 9 over 20(a - 1)

• 45 over 10(a - 1)

Why is it important to simplify both the numerator and the denominator in rational expressions?

• To find the simplest form of the expression

• To increase the value of the expression

• None of the above

• To make the expression more complex